Algebra-Functions and Equations (InterMath)
Melanie is shopping for work clothes.
She has found a dress for $75 and a two-piece suit
for only $60. She does not have enough money for both, so she
must choose only one.
Of course, both are "dry clean only."
If her dry cleaner charges $4.50 for a dress and
#3 for each piece of suit, which will be a better deal in the
How many times will she have to dry clean the purchased
item before it is the better deal?
x= number of times the garment is dry-cleaned
f(x)= 4.50x + 74
g(x) = 6x + 60
Set the two equations equal to each other and you get
a point of intersection.
This point of intersection is where the garments would
be costing the same amount in the "long run."
4.5x + 75 = 6x + 60
4.5x + 15 = 6x
15 = 1.5 x
10 = x
At the 10th dry cleaning the garments would cost
exactly the same.
After that point, the dress (which originally cost
more) would be more economical and financial friendly. :)
Melanie would have to dry clean her chosen item
11 times to make the dress the better deal in the long run.
Solution shown graphically:
This solution shows that the two garments would
cost exactly the same at the 10th dry cleaning also...because
you cannot dry clean an item 9.33 times...you must round up from
9 to 10.
The answer still remains that Melanie would have
to dry clean her chosen item 11 times to make the dress the better
deal in the "long run."